'Regular' milk will not spoil in a day if kept in a similar (clean) flask. UHT milk should/will last longer than regular milk, given the same handling.
Cold does not stop spoilage...it merely slows it down. Keep all foods out of the sun, away from bugs, and ensure foodware, utensil and hands are clean and your food can last a long time on the trail.
Meanwhile...do an at-home experiment. Set the milk-filled flask on the counter or outside and find out how long it lasts...
I acknowledge the desirability of keeping UHT milk cold. Super cold was the only way I could tolerate it.